Here are your parts
Parts for Whirlpool DU1055XTSS2 Dishwasher - AppliancePartsPros.comSee the attachment for your tech sheet.
That the unit used to fill in one cycle type but not others points towards a bad control board, but I would do the valve checks just in case it is something weird.
Check that the float switch is being activated (closed)
Sometimes the float can get stuck in the up position. If it is then usually cleaning it will fix the problem.
If the overfill switch is being activated, check for 120 volts across the fill valve when it should be filling.
If there is no voltage, check across the fill valve/overfill switch combo (wired in series)
If there is no voltage there, then the control board is probably toast.
If there is voltage, then check across the overfill switch. If there is voltage across the switch then the switch is shot.
I would check the wires from the parts that go up to the control board for continuity, just in case it is a bad wire.
If there is 120 volts across the fill valve then either the fill valve needs replacing or it's filter needs cleaning.
There is a screen filter built into the input side of the valve. Remove the valve from the unit and check/clean the screen filter.
Do not permanently remove the screen filter from the valve as it is there to keep crud out of the valve which could hold it open and cause a flood.
If all the above are OK then I would replace the control board.
If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.
4. When you start always short the meter leads together. This will tell you that the meter is working and if there is any 0 offset.
There is a good STICKY at the start of this forum about it's use.